Tenths and Hundredths: a week of ready-to-teach maths

Five days of lessons for Year 4 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out squares, strips and cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the two card sheets once; the squares, strips and cards are reused all week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week is short: place value does not stop at the ones. Split one whole into ten equal parts and each part is a tenth; split a tenth into ten and each part is a hundredth. The decimal point sits just after the ones and marks where the parts begin.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

How we say decimals

This pack reads 0.6 as “six tenths” and 0.06 as “six hundredths”, so the place is in the name. “Zero point six” is also fine once children know what the six is worth. A decimal less than one is written with a zero before the point: 0.6, not .6.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 makes tenths from one whole; Day 2 makes hundredths from a tenth; Day 3 lines the places up across the point; Day 4 gives every decimal a place on the number line, so it can be compared and ordered; and Day 5 names decimals aloud and in money. It builds on the Year 3 place value beyond 10 000 and on unit fractions, and it is the place value that fractions as decimals, measuring and money lean on for the rest of Year 4.

Materials for the week (one trip)

• From the classroom: scissors, pencils, coloured pencils, this pack printed.
• For Day 4: a strip of masking tape along the floor marked 0 and 1, and sticky notes for the tenth marks (optional).
• For Day 5: a few real coins and a supermarket docket or catalogue (optional).
• Cut out once, use all week: the whole squares and tenth strips, the decimal place-value cards and the decimal cards in this pack. No maths equipment to buy.

Words for the word wall

whole, equal parts, tenth, hundredth, decimal, decimal point, ones, place, digit, number line, between, dollars, cents

Dear families

This week in maths, Year 4 meets tenths and hundredths. We split one whole into ten and a hundred equal parts, write the parts as decimals such as 0.3 and 0.45, find them on a number line and say them aloud. Money helps: a cent is one hundredth of a dollar.

Try this at home

• Read a price together, such as $3.45, and ask what each digit is worth: 3 dollars, 4 ten-cent pieces, 5 cents.
• Cut a slice of toast or a sheet of paper into ten equal strips. Eat or colour three: that is three tenths, 0.3.
• Count by tenths while you walk: 0.1, 0.2, 0.3 and on past 1: 1.1, 1.2. After nine tenths comes one whole.
• Ask which is more, 0.5 or 0.35. Compare the tenths first.

My decimals this week

Fill one row a day. Find a decimal at home (a price, a measure, a score) and pull it apart.

Printed from the free seegongsik Tenths and Hundredths teaching pack · seegongsik.com/au/y4/number/AC9M4N01/pack

One whole, ten tenths

Children split one whole into ten equal parts, name each part a tenth, and write tenths as fractions and as decimals. Then they count by tenths up to one whole and past it.

We are learning to

• explain that a tenth is one of ten equal parts of one whole,
• write a number of tenths as a fraction and as a decimal (3 tenths is 3/10 and 0.3),
• count by tenths past one: 0.9, 1, 1.1, 1.2.

Success criteria

• I can shade a number of tenths and write it as a decimal.
• I can count on by tenths across one whole.

You need

The tenth strips cut from one whole square (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by shading the board bar again.

Watch for these ideas

• Parts that are not equal. A tenth is one of ten equal parts; ten pieces of any size are not tenths.
• Writing three tenths as 0.03 or 3.0. The first place after the point is the tenths.
• Counting 0.8, 0.9, 0.10. Ten tenths make one whole, so the count goes 0.9, 1, 1.1.

Answers

• Part A: 0.4 = 4/10; 0.7 = 7/10; 1 (or 1.0) = 10/10.
• Part B: shade 6 parts for 0.6, 2 parts for 0.2, 9 parts for 0.9; the fractions are 6/10, 2/10, 9/10.
• Part C: 0.9, 1, 1.1, 1.3. Part D: 10 tenths; 14 tenths; 20 tenths; 2.5.

Shade the tenths

Each bar is one whole split into ten equal parts. Each part is one tenth.

A. How much is shaded?

B. Shade it

C. Count on by tenths

0.7,  0.8,  ______,  ______,  ______,  1.2,  ______

D. How many tenths?

1 whole = ______ tenths     1.4 = ______ tenths     2 = ______ tenths

25 tenths make the decimal ______

Cut a tenth into ten

Children cut one tenth strip into ten little squares and find that each is one hundredth of the whole. They read a hundred-square as tenths (full columns) and hundredths (loose squares), and see that 0.4 and 0.40 are the same amount.

We are learning to

• explain that a hundredth is one of a hundred equal parts of one whole, a tenth cut into ten,
• say how many tenths and hundredths a decimal like 0.27 has,
• show that ten hundredths make one tenth, so 0.4 = 0.40.

Success criteria

• I can shade a decimal with hundredths on a hundred-square.
• I can say how many tenths and hundredths it has.

You need

A second whole square from cut-out sheet 1, cut into strips, and one strip cut into ten squares, per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after 0.27; start Session B with 0.35 on the square.

Watch for these ideas

• Reading 0.27 as “twenty-seven tenths”. It is 27 hundredths: 2 tenths and 7 hundredths.
• Thinking 0.08 is more than 0.5 because 8 is more than 5. Compare the tenths first: 0 against 5.
• Thinking 0.40 is more than 0.4. The zero hundredths add nothing.

Answers

• Part A: 0.36 = 3 tenths and 6 hundredths; 0.09 = 0 tenths and 9 hundredths; 0.80 = 8 tenths and 0 hundredths. Part B: 0.52 is 5 columns and 2 squares; 0.70 is 7 columns and 0 squares.
• Part C: 10; 30; 6 tenths; 45 hundredths. Part D: same; different; same; different.

Tenths and hundredths on the square

Each big square is one whole. A column is one tenth. One little square is one hundredth.

A. Read the square

B. Shade it

C. Ten hundredths make one tenth

0.1 = ______ hundredths     0.3 = ______ hundredths

0.60 = ______ tenths     4 tenths and 5 hundredths = ______ hundredths

D. Same amount or different? Circle one.

0.5 and 0.50:  same / different      0.7 and 0.07:  same / different

0.30 and 0.3:  same / different      0.9 and 0.09:  same / different

Across the point

Children line digits up in a place-value chart: ones, then the decimal point, then tenths and hundredths. They read a decimal by its places, build it with place-value cards and write it as a sum of its places.

We are learning to

• name the places on each side of the decimal point: ones, tenths, hundredths,
• say what each digit of a decimal is worth (in 3.27 the 2 is two tenths),
• write a decimal as a sum of its places, with a zero holding an empty place.

Success criteria

• I can read a decimal by its places.
• I can build a decimal with cards and write it as a sum.

You need

The decimal place-value cards (cut-out sheet 2), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after 1.06; start Session B by reading 2.80 off the chart.

Watch for these ideas

• Writing 1.06 as 1.6. Without the zero, the 6 slides into the tenths and is worth ten times more.
• Reading 2.80 as “two point eighty”. Read the digits after the point one at a time: two point eight zero.
• Thinking more digits means a bigger number (2.45 against 3.1). The ones decide first.

Answers

• Part A: 0.45 = 0.4 + 0.05; 1.06 = 1 + 0.06; 2.80 = 2 + 0.8; 5.13 = 5 + 0.1 + 0.03; 0.09 = 0.09.
• Part B: 2.53; 0.04; 7.10 (or 7.1); 6.38. Part C: 6 ones; 6 tenths; 6 hundredths; 6 hundredths.

Build it across the point

Build each number with your place-value cards. Write each digit in its place, then write the number as a sum.

A. The place-value chart

B. Build it from the places

2 ones, 5 tenths, 3 hundredths = __________     0 ones, 0 tenths, 4 hundredths = __________

7 ones, 1 tenth, 0 hundredths = __________     6 + 0.3 + 0.08 = __________

C. What is the 6 worth?

In 6.2: ______________     In 0.6: ______________

In 0.06: ______________     In 3.16: ______________

Every decimal has an address

Children find a decimal on a number line in two moves: first the tenth it falls in, then a zoom in to count the hundredths. Further along the line always means larger, so they use the line to compare and order decimals.

We are learning to

• name the two tenths a decimal sits between (0.47 is between 0.4 and 0.5),
• zoom in on one tenth and count hundredths to place a decimal exactly,
• compare and order decimals by their tenths first, then their hundredths.

Success criteria

• I can place a decimal between two tenths on a number line.
• I can put four decimals in order, smallest first.

You need

The decimal cards (cut-out sheet 2), one set per group of four. A floor line of tape marked 0 and 1 (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by zooming in on 0.4 to 0.5.

Watch for these ideas

• Thinking 0.23 is more than 0.8 because 23 is more than 8. Compare the tenths: 2 against 8.
• Placing 0.47 between 4 and 5. The line runs from 0 to 1; every mark is a tenth.
• Counting the marks instead of the jumps when zoomed in. Start at 0.4 and count the jumps.

Answers

• Part A: 0.23 is between 0.2 and 0.3; 0.65 is between 0.6 and 0.7; 0.8 sits on the mark for 8 tenths. Part B: 0.42 and 0.47 are 2 and 7 jumps past 0.4; 0.65 and 0.69 are 5 and 9 jumps past 0.6.
• Part C: 0.6 > 0.58; 0.07 < 0.7; 0.35 < 0.4; 1.2 > 0.99. Part D: 0.04, 0.14, 0.4, 0.44.

Find each decimal’s address

A. Mark 0.8, 0.23 and 0.65 with an arrow

0.23 is between ______ and ______     0.65 is between ______ and ______

0.8 sits right on the mark for ______ tenths.

B. Zoom in and count the hundredths

Mark 0.42 and 0.47.

Mark 0.65 and 0.69.

C. Write <, > or =

0.6 ____ 0.580.07 ____ 0.70.35 ____ 0.41.2 ____ 0.99

D. Put them in order, smallest first

0.4,  0.04,  0.44,  0.14

__________,  __________,  __________,  __________

Say it, write it, spend it

Children read decimals aloud so the place is in the name (six tenths, six hundredths), explain why a zero on the end changes nothing, and write prices as dollars and cents. A cent is one hundredth of a dollar, so money always shows two places after the point.

We are learning to

• say a decimal in words by its smallest place (0.27 is twenty-seven hundredths),
• explain that 0.4 and 0.40 name the same amount,
• write a price in dollars and cents with two decimal places ($2.05).

Success criteria

• I can say a decimal in words and write it from words.
• I can write a price with two places after the point.

You need

The decimal place-value cards (cut-out sheet 2). A few real coins or a supermarket docket (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B by reading $3.45 aloud.

Watch for these ideas

• Saying 0.06 as “six tenths”. The 6 is in the hundredths place: six hundredths.
• Writing 2 dollars and 5 cents as $2.5. The cents take two places: $2.05.
• Thinking the zero on the end of 0.40 makes it bigger. A price keeps the zero to show the cents; the amount is the same as 0.4.

Answers

• Part A: four tenths = 0.4; four hundredths = 0.04; two and five tenths = 2.5; nineteen hundredths = 0.19; one and six hundredths = 1.06. Part B: eight tenths; thirty-five hundredths; nine hundredths; three and seven tenths.
• Part C: 50 cents; $2.05; $0.85; $7.30; 10 dollars and 9 cents. Part D: $1.95; $0.50; $4.90.

Say it, write it, spend it

A. Write the decimal

four tenths = __________

four hundredths = __________

two and five tenths = __________

nineteen hundredths = __________

one and six hundredths = __________

B. Write it in words

0.8 = ________________________    0.35 = ________________________

0.09 = ________________________    3.7 = ________________________

C. Dollars and cents

$4.50 is 4 dollars and ______ cents.

2 dollars and 5 cents = $__________

85 cents = $__________

7 dollars and 30 cents = $__________

$10.09 is ______ dollars and ______ cents.

D. Which costs more? Circle it.

$1.95 or $1.59      $0.50 or $0.05      $4.09 or $4.90

Tell your partner how you knew, using the words tenths and hundredths.

Two whole squares

Each big square is one whole. Cut the first square along its thick lines into ten strips: each strip is one tenth (Day 1). Cut the second square into strips too, then cut one strip along its thin lines into ten little squares: each little square is one hundredth (Day 2). One sheet per pair.

Teacher note: keep the strips and squares in an envelope per pair. A whole square, a strip and a little square are one, one tenth and one hundredth, the same picture as “A tenth into a hundred” on screen.

Place-value cards and decimal cards

Cut out the cards. To build a decimal, lay one card from each row side by side and read them as a sum: 3 and 0.2 and 0.07 make 3.27. Leave a row out when its place is empty: 1 and 0.06 make 1.06.

Ones

Tenths

Hundredths

Decimal cards (Day 4)

Teacher note: the decimal cards hold the four numbers from “Find it on the line” (0.47, 0.8, 0.23, 0.65) and look-alike pairs such as 0.4 and 0.04, 1.06 and 1.6. Ask groups to order all twelve, smallest first.

What we know: Tenths and Hundredths

Work on your own. Show your thinking if you can.

1. In 4.38, the 3 is worth ________________ and the 8 is worth ________________.
2. The square is one whole. Write the shaded part as a decimal: __________
3. How many hundredths make one tenth? ______   How many tenths make one whole? ______
4. Write 7 + 0.4 + 0.05 as one decimal: __________   Write 2 ones and 9 hundredths: __________
5. 0.58 is between the tenths ______ and ______.
6. Write <, > or = :   0.9 ____ 0.85    0.07 ____ 0.7    0.50 ____ 0.5
7. Put these in order, smallest first: 0.6, 0.06, 0.66, 0.16.   __________________________
8. Write the price: 6 dollars and 5 cents = $__________   $12.40 is ______ dollars and ______ cents.

Answers and marking guide

Answers

1. 3 tenths (0.3) and 8 hundredths (0.08).
2. 0.34: 3 full columns and 4 little squares, so 3 tenths and 4 hundredths.
3. 10 hundredths make one tenth; 10 tenths make one whole.
4. 7.45; 2.09 (the zero holds the empty tenths).
5. 0.5 and 0.6 (it has 5 tenths and 8 hundredths).
6. 0.9 > 0.85 (9 tenths against 8); 0.07 < 0.7; 0.50 = 0.5.
7. 0.06, 0.16, 0.6, 0.66.
8. $6.05 (the cents take two places); 12 dollars and 40 cents.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, naming the place of each digit.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: tenths, hundredths, the chart, the number line, and names and prices.